Being a Student Nurse is making me fear death more. Help?

I'm currently in my first year of nursing and I haven't seen any deaths yet. I've done the last offices and seen people at the end of life but not actually seen them die. However, when I was 9 I seen both my grandmas die on the same week so it isn't something new to me. Before starting nursing, I've always had a fear and anxiety over my mum and dad dying and I think it's because I'm an only child. However, starting nursing (even though I haven't seen any deaths, even having a placement in a ICU), it's making me fear growing older and being at the end of life and dying myself, even at my young age now, but also it's heightened my fear of my parents dying and ones around me. Does anyone else have these fears? I'm scared that being in these environments and being a nurse is making me fear it more than actually helping me get over it. Is this something I can carry on with and get over? I love every other aspect of being a nurse but it has make me thinking about death and older life more, in a negative way. I'd appreciate any advice.